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Towards a methodology for measuring the true degree of efficiency in a speculative market

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Journal of the Operational Research Society

Abstract

Betting markets have drawn much attention in the economics, finance and operational research literature because they provide a valuable window on the manner in which individuals use information in wider financial markets. One question that has received particular attention is to what extent individuals discount information in market prices. The predominant approach to explore this issue involves predictive modeling to forecast market outcomes and examining empirically whether abnormal returns can be made by employing these forecasts. It is argued here that present practices to assess such forecasting models, including the use of point estimates and information, which would not be available in practice (at the forecasting stage) and failing to update forecasting models with information from the recent past, may give rise to misleading conclusions regarding a market's informational efficiency. Hypotheses are developed to conceptualize these views and are tested by means of extensive empirical experimentation using real-world data from the Hong Kong horserace betting market. Our study identifies several sources of bias and confirms that current practices may not be relied upon. A more appropriate modeling procedure for assessing the true degree of market efficiency is then proposed.

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Notes

  1. Measuring the true degree of market efficiency requires that practical considerations for exploiting information are considered. Consequently, a day-wise rather than a race-wise jackknife is employed because the latter would imply that individual forecasting models could be built for each race. This is practically impossible given that informative odds, which form an important part of these models, are only available at most 5 min before the start of a race.

  2. Equivalent to the homogeneity of variance assumption in ordinary (ie, between-subjects) ANOVA.

  3. This follows from the fact that the results observed for a training-set size of 100 racing days (ie, ∼700 races) does not differ significantly from those observed for any larger setting.

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Authors and Affiliations

  1. University of Hamburg, Hamburg, Germany

    S Lessmann

  2. University of Southampton, Southampton, UK

    M-C Sung & J E V Johnson

Authors
  1. S Lessmann
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  2. M-C Sung
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  3. J E V Johnson
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Corresponding author

Correspondence to S Lessmann.

Appendices

Appendix A

Data characteristics and independent variables

The data set employed in the study embraces 4276 races with 55 690 runners. The data set incorporates a rich set of different types of horseraces, varying in, for example, distance, race class, track conditions and surface, as well as time of race (ie, day or night) or race type (ie, handicap versus non-handicap). Table A1 summarizes the distribution of races across these factors as well as their evolution over time.

Table A1 Data characteristics and their evolution over time
Full size table

In order to construct CL forecasting models, a set of 40 fundamental variables has been employed, which are designed to capture each runner's winning potential. Whereas the precise nature of the variables is not important here (since our aim is to demonstrate that different methodologies associated with model training and testing, and associated wagering strategies, have a significant effect on the degree of efficiency identified in a market), a brief summary of their definition is given in Table A2. In addition to these fundamental variables, all forecasting models also incorporate runners’ market odds.

Table A2 Summary of independent variables employed in the empirical evaluations
Full size table

Appendix B

Detailed results of the learning curve analysis

See Table B1.

Table B1 Development of ROR across different training- and test-set sizes within a learning curve analysis
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Lessmann, S., Sung, MC. & Johnson, J. Towards a methodology for measuring the true degree of efficiency in a speculative market. J Oper Res Soc 62, 2120–2132 (2011). https://doi.org/10.1057/jors.2010.192

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